This invention relates to nuclear magnetic resonance (NMR) measurements and, more particularly, analysis of NMR data.
NMR has been a common laboratory technique for over forty years and has become an important tool in formation evaluation. General background of NMR well logging can be found, for example, in U.S. Pat. No. 5,023,551 to Kleinberg et al., which is assigned to the same assignee as the present invention and herein incorporated by reference in its entirety.
NMR relies upon the fact that the nuclei of many chemical elements have angular momentum (xe2x80x9cspinxe2x80x9d) and a magnetic moment. In an externally applied static magnetic field, the spins of nuclei align themselves along the direction of the static field. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field (e.g., a RF pulse) that tips the spins away from the static field direction. The angle through which the spins are tipped is given by xcex8=xcex3B1tp/2, where xcex3 is the gyromagnetic ratio, B1 is the linearly polarized oscillating field strength, and tp is the duration of the pulse. Tipping pulses of ninety and one hundred eighty degrees are most common.
After tipping, two things occur simultaneously. First, the spins precess around the direction of the static field at the Larmor frequency, given by xcfx890=xcex3B0, where B0 is the strength of the static field and xcex3 is the gyromagnetic ratio. For hydrogen nuclei, xcex3/2xcfx80=4258 Hz/Gauss, so, for example, in a static field of 235 Gauss, the hydrogen spins would precess at a frequency of 1 MHz. Second, the spins return to the equilibrium direction according to a decay time, T1, which is known as the spin-lattice relaxation time. Because this spin-lattice relaxation occurs along the equilibrium direction, T1 is also referred to as the longitudinal relaxation time constant.
Also associated with the spin of molecular nuclei is a second relaxation time, T2, called the spin-spin relaxation time. At the end of a ninety-degree tipping pulse, all the spins are pointed in a common direction perpendicular, or transverse, to the static field, and they all precess at the Larmor frequency. However, because of small fluctuations in the static field induced by other spins or paramagnetic impurities, the spins precess at slightly different frequencies, and the transverse magnetization dephases with a time constant T2, which is also referred to as the transverse relaxation time constant.
A standard technique for measuring T2, both in the laboratory and in well logging, uses a RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is well known, after a wait time that precedes each pulse sequence, a ninety-degree pulse tips the spins into the transverse plane and causes the spins to start precessing. Then, a one hundred eighty-degree pulse is applied that keeps the spins in the measurement plane, but causes the spins, which are dephasing in the transverse plane, to reverse direction and to refocus. By repeatedly reversing the spins using a series of one hundred eighty degree pulses, a series of xe2x80x9cspin echoesxe2x80x9d appear. The train of echoes is measured and processed to determine the irreversible dephasing time constant, T2. In well logging applications, the detected spin echoes have been used to extract oilfield parameters such as porosity, pore size distribution, and oil viscosity.
In theory, other laboratory NMR measurements may be applied in well-logging to extract additional information about the oilfield, but in practice, the nature of well-logging and the borehole environment make implementing some laboratory NMR measurements difficult. For example, inversion recovery is a common laboratory technique for measuring T1. In an inversion recovery measurement, a one-hundred eighty degree pulse is applied to a system of spins aligned along the static magnetic field in order to reverse the direction of the spins. The system of spins thus perturbed begins to decay toward their equilibrium direction according to T1. To measure the net magnetization, a ninety-degree pulse is applied to rotate the spins into the transverse plane and so induce a measurable signal. The signal will begin to decay as the spins dephase in the transverse plane, but the initial amplitude of the signal depends on the xe2x80x9crecovery timexe2x80x9d between the one-hundred eighty degree pulse and the ninety-degree pulse. By repeating this experiment for different recovery times and plotting the initial amplitude of the signal against recovery time, T1 may be determined. While this technique has been successfully used in the laboratory for several years, inversion recovery is very time consuming, and those of ordinary skill in the art recognize that inversion recovery may be unsuitable for well logging applications.
Accordingly, there continues to be a general need for improved NMR measurements and, in particular for the oil and gas exploration industries, improved NMR methods that can be used to extract information about rock samples and be used in well-logging applications.
The invention provides a method for extracting information about a system of nuclear spins, such as in a fluid that may be contained in a rock or within a portion of earth formation surrounding a borehole (as used hereinafter, the term xe2x80x9crockxe2x80x9d includes earth, earth formation, and a portion of earth formation), or other porous environment. The method involves performing at least one nuclear magnetic resonance measurement on a system of nuclear spins and acquiring nuclear magnetic resonance data from each of the measurements. The nuclear magnetic resonance data are expressed using a kernel that is separable along at least two dimensions, compressed along each dimension of the kernel, and then analyzed to extract information about the system of spins.
Further details and features of the invention will become more readily apparent from the detailed description that follows.